VM-LSDYNA-SOLVE-009
VM-LSDYNA-SOLVE-009
Steady State Thermal Analysis with Convection between Surfaces
Overview
| Reference: | Kreith, F. (1959). Principles of Heat Transfer (2nd ed.). International Textbook Co. |
| Analysis Type(s): | Steady State Thermal |
| Element Type(s): | Bulk Node |
| Input Files: | Link to Input Files Download Page |
Test Case
A fluid with volume Vc = 1.0 m3 is contained between two surfaces. Surface A has area Aa = 1 m2, heat transfer coefficient ha = 1.0 W/(m2°C), and temperature Ta = 1°C. Surface B has area Ab = 2 m2, heat transfer coefficient hb = 2.0 W/(m2°C), and temperature Tb = 2°C. Heat is transferred to the fluid through convection. Find the steady state temperature of the fluid Tc.
| Material Properties | Geometric Properties | Loading |
|---|---|---|
| ha = 1 W/(m2°C) | Vc = 1.0 m3 | Ta = 1°C |
| hb = 2 W/(m2°C) | Aa = 1.0 m2 | Tb = 2°C |
| — | Ab = 2.0 m2 | — |
Analysis Assumptions and Modeling Notes
LS-DYNA Thermal Solver 1 is used. The elements containing surfaces A and B are modeled using ELFORM 1. The fluid between surfaces is modeled using *BOUNDARY_THERMAL_BULKNODE where heat flow between the bulk node and node segments, surface A and B, is given by the convection equation.
At steady state, the rate of heat dissipation Q:
And the thermal resistances Rac and Rcb can be expressed as:
From the above equations, the analytical solution of Tc is obtained as 1.8°C